Tag: desmos

Visualizing Shared Work Problems

Post author By Bob Lochel
Post date September 30, 2013
2 Comments on Visualizing Shared Work Problems

Fred can paint a room in 5 hours, working alone. His friend, Joe, can paint the same room in 7 hours. How long will it take for them to paint the room, working together?

It’s a shared-work party, people! Get your party hats on and let’s look at a visual method for exploring these often mundane problems. This past summer at Twitter Math Camp, I participated in an algebra 2 group where part of our time was spend considering methods to re-think the traditionl approach to rational functions and their applications. Thanks to John Berray for the great conversations, which led to some changes in how I appoached shared work problems this year.

My approach this year started similarly to previous years: guiding a dicussion with the class, with the goal of developing models for the amount of work done by each painter. I find that quesitons like “How much of the job will fred have complete after 1 hour? 2 hours…etc” will usually lead to the models we seek. What I did differently this year was graph the two work functions. Using the Desmos calculator works nicely, and allowed for a discussion of the problem much richer than if the expressions had been just jotted down on the board. Many students followed along on their TI calculators.

SW1

From here, we can make connections betweem the functions, their graphs, and make conjectures about the sum of these functions.

SW2

In my class, students certainly completed similar problems (including distance / rate / time), with the graphs serving as a check and visual affirmation. With the graphs, we could also look at adaptations to the theme, such as “what happens if one of the painters shows up 2 hours late?”

SW3

Also, problems where the combined time was given, with the goal of finding a missing individual rate, were explored and discussed.

SW4

Click the icon below to play with this model on your own. This is a great opportunity to let students observe function behavior and communicate results from a graph.

UPDATE: The Desmos folks flew with this one, and added a whole bunch of bells and whistles. Click the graph below to experience their shared-work extravaganza.

Tags algebra 2, desmos, rational functions

High School Technology

Use Appropriate Tools Strategically

Post author By Bob Lochel
Post date September 10, 2013
1 Comment on Use Appropriate Tools Strategically

This semester, my Algebra 2 students will be exposed to a wealth of math tech tools. Graphing calculators will be a big part of what happens in my classroom; not only because they are great tools for discovery, but also because I feel some responsibility to have students understand the appropriate use of these tools as they head towards AP classes. Forcing a tool upon students because it will help them on a test is weak, I know…I cry myself to sleep sometimes…though I do rely on the technology to craft discovery moments in my class.

But I also want my students to experience other tools, like the Desmos calculator (which we will use later for the world-famous Conic Sections project), Geogebra and Wolfram|Alpha (reviewed earlier here on the blog). So, how do I get my students to experience all of these tools, and start to make measured decisions about how and when to use them? Hey, we have a Standard for Mathemaical Practice for that!

CCSS.Math.Practice.MP5 Use appropriate tools strategically.

Lost in the great stuff on precision, modeling and reasoning is this awesome nugget, with a specific focus on tech tools:

Mathematically proficient students at various grade levels are able to identify relevant external mathematical resources, such as digital content located on a website, and use them to pose or solve problems. They are able to use technological tools to explore and deepen their understanding of concepts.

Nice! Exactly what I am looking for! So, how do you do that? How do you get students to start comparing and assessing tools?

Here is the day 1 assignment I gave to my students in Algebra 2, as posted on Edmodo:

Write a product review for the Desmos online calculator. Consider its pros and cons, and whether you feel this is a site you would recommend to others. One side of a piece of paper MAX. Screen shots allowed and encoraged. Can be turned in via hard copy, or electronically.

Thats it. Go ahead, kick the tires, and tell me what you find. I didn’t make students aware of my on-going man-crush with Desmos or that I had done a webinar for them. I had no idea what I was going to get back. And since I stress written communication in my classes (moreso, I suppose, than many math teachers), this gave me a first writing sample to analyze.

The results were largely encouraging. While many students focused solely on the graphing of functions, some students demonstrated evidence of digging deeper, looking for characteristics which make Desmos unique. Some snippets:

Unlike the normal graphing calculator, it graphs your equation as you are typing it and allows you to delete parts of the equation if your graph isn’t what you wanted it to be. Desmos also provides the general equations for many different lines, parabolas, and other more advanced graphs.

The example graph list on the left side of the screen acts as a jump start and learning tool to give confused students a boost in the right direction.

It is quick, simple, and efficient to use and is recommended to all users that seek a tool for graphing. The designs are not distracting but sleek and a simple white to emphasize the purpose of the tool, for math and nothing else.

The Desmos is different, its not complicated at all, it can do so many things that most calculators can’t, and it’s free. The fact that Desmos is free is really what makes it so much better than all of the other because you don’t have to shell $120 out of your pocket for a calculator that has all the same capabilities that Desmos has.

But not all is sunny, as some students noted some “Cons”:

With the internet calculator, there is the obvious issue of no internet, no calculator. Also, I found some buttons were tough to get to such as the “pi” key which required me to press several buttons in order to get that one.

One last thing about the calculator is the fact that it can be downloaded as an app, but only on apple products. For android users, like myself, you would have to use the calculator through the internet which isn’t as easy to use as through an app. Also, the app is accessible without wireless internet connection, but android users need the wireless connection to use the Desmos calculator.

All told, a good first writing assignment for my students, followed by some discussions of tools and their appropriate use. As we travel through Algebra 2, many chances to compare tools, and discuss the best tool for the job. Looking forward to doing another product review, using Wolfram|Alpha. Stay tuned.